Speaker John Boehner’s counter-offer to President Obama’s proposal on averting the fiscal cliff was an instant non-starter. But quietly, Boehner may be positioning himself to get a deal with the White House.

Monday, Boehner sent a letter to Obama that proposed unspecified spending cuts of $1.2 trillion, and new tax revenue of $800 billion, to be achieved through changes to the tax code, while lowering tax rates for the rich. The Speaker was responding to an administration proposal, offered Friday, that would include far less in spending cuts, and would raise $1.6 trillion in tax revenue by upping rates on the richest Americans.

Just as Republicans had dismissed that proposal, the White House quickly rejected Boehner’s, saying it “does not meet the test of balance.”

That appears to leave negotiations on the fiscal cliff right where they started. But behind the scenes, Boehner is bolstering his own standing within the GOP caucus at the expense of the party’s most conservative members.

A group of conservative Republicans who had not always voted with the party’s leadership lost their posts on key committees Monday—an effort by Boehner to increase the pressure on GOP lawmakers to toe the party line.

A GOP aide told Roll Call that the message of the move was: “You want good things in Congress and to have a good career? Better play along nicely.”

Pressure from the Tea Party caucus within the GOP, many of whom were elected in 2010, has been the main factor preventing Boehner from compromising with Obama on budget issues. If he succeeds in reducing that pressure, it may well make a deal more likely.